2006.50: Curve Crossing for the Reflected Process

Abstract

Let R_n = max0<=j<=n S_j − S_n be a random walk S_n reflected in its
maximum. We give necessary and sufficient conditions for finiteness of passage times of Rn above horizontal or certain curved (power law) boundaries. Necessary and sufficient conditions are also given for the
finiteness of the expected passage time of R_n above linear and square root boundaries.

Item Type:

MIMS Preprint

Uncontrolled Keywords:

Reflected process, rate of growth, renewal theorems, power law
boundaries.